1993

《紐約嫻情》是香港女歌手陳慧嫻,於 1993 年拍攝的音樂特輯;監製金廣誠,編導盧冰心;香港時間 1993 年 10 月 10 日(星期日)晚上 8 時至 9 時 05 分,於香港無綫電視翡翠台首播。

這個節目是為了,讓歌迷認識並了解,當年正值如日中天,卻遠赴美國讀書的陳慧嫻,在美國紐約的點滴。節目形式為邊播放,陳慧嫻的多首經典歌曲,並拍攝她在紐約多處地方留下的倩影。然後在每首歌曲播放完結後,有慧嫻的自白,剖析她在美國獨自生活的一點一滴。

節目合共播放 11 首陳慧嫻的歌曲;按出場序排列:

《千千闋歌》
《傻女》
《花店》
《Joe le Taxi》
《飄雪》
《碎花》
《人生何處不相逢》
《Jealousy》
胡思亂想
《紅茶館》
《幾時再見?!》

陳慧嫻在節目介紹,她在美國的公寓、同學以及交通等生活背景,首先解釋留學讀書的原因。由於其父母希望陳慧嫻,除了唱歌外有其他技能,例如做生意,所以要求她完成大學學業,令自己不再當歌手,亦能有謀生技能。又提到其前男友歐丁玉,曾在她早期陪伴她讀書。其後由於區娶了另一女子,令陳慧嫻對於感情生活,有很大的感觸,不斷強調要珍惜眼前人,又指感情生活難以估計,因此會嘗試適應獨自生活。另指出之後重返樂壇,將以不同心態迎接,順其自然。

— 文字在創用 CC 姓名標示-相同方式分享 3.0 協議之條款下提供,附加條款亦可能應用。

— 維基百科

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When this music special premiered in 1993, my TV was showing it in the background while I was having my dinner. I was not watching it. So I did not know the content. But still, I remembered the atmosphere broadcast by it.

In an afternoon in 1996, it was broadcast again. I took a VCR cassette at once to record it. However, I was already a few minutes late, missing the first part of the show.

I watched this music special after every last exam.

In 200x, I bought a TV card just to transfer the music special from the VCR to my computer. However, I have already lost both the VCR cassette and the computer file.

— Me@2022-01-26 09:30:53 PM

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2022.01.26 Wednesday ACHK

2.10 Extra dimension and statistical mechanics

A First Course in String Theory

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Write a double sum that represents the statistical mechanics partition function \displaystyle{Z(a, R)} for the quantum mechanical system considered in Section 2.10. Note that \displaystyle{Z(a, R)} factors as \displaystyle{Z(a, R) = Z(a) \tilde{Z}(R)}.

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Eq. (2.118):

\displaystyle{  \begin{aligned}  - \frac{\hbar^2}{2m} \frac{1}{\psi(x)} \frac{d^2 \psi(x)}{dx^2}   - \frac{\hbar^2}{2m} \frac{1}{\phi(x)} \frac{d^2 \phi(x)}{dx^2}   &= E \\   \end{aligned}}

\displaystyle{  \begin{aligned}  \psi_{k, l} (x,y) &= \psi_k (x) \phi_l (y) \\   \end{aligned}}

Eq. (2.119):

\displaystyle{  \begin{aligned}  \psi_k (x) &= c_k \sin \left( \frac{k \pi x}{a} \right) \\   \end{aligned}}

\displaystyle{  \begin{aligned}  \frac{d^2 \psi_k (x)}{dx^2} &= - \left( \frac{k \pi}{a} \right)^2 \psi_k (x) \\   \end{aligned}}

\displaystyle{  \begin{aligned}  - \frac{\hbar^2}{2m} \frac{1}{\psi(x)} \frac{d^2 \psi(x)}{dx^2}   - \frac{\hbar^2}{2m} \frac{1}{\phi(x)} \frac{d^2 \phi(x)}{dx^2}   &= E \\     \frac{\hbar^2}{2m} \left( \frac{k \pi}{a} \right)^2   + \frac{\hbar^2}{2m} \left( \frac{l}{R} \right)^2   &= E \\     \end{aligned}}

\displaystyle{    \begin{aligned}    E   &=     \frac{\hbar^2}{2m} \left[ \left( \frac{k \pi}{a} \right)^2 + \left( \frac{l}{R} \right)^2 \right] \\    \end{aligned}}

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[guess]

Index \displaystyle{k = 1, 2, \dotsb} but not negative integers because, for example, k = 1 and k=-1 give physically identical states

\displaystyle{  \begin{aligned}  \psi_{-1} (x) &= c_{-1} \sin \left( \frac{- \pi x}{a} \right) \\   \end{aligned}} and \displaystyle{  \begin{aligned}  \psi_{1} (x) &= c_{1} \sin \left( \frac{\pi x}{a} \right) \\   \end{aligned}}.

The two wave functions give the same probability density distribution, if c_{-1} = c_{1}.

However, that is not the case for

\displaystyle{  \begin{aligned}  \phi_l(y) &= a_l \sin \left(\frac{ly}{R}\right) + b_l \cos \left(\frac{ly}{R} \right) \\   \end{aligned}}.

So l should have also negative integers as possible values: l = \dotsb, -2, -1, 0, 1, 2, \dotsb.

[guess]

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Eq. (2.120):

\displaystyle{  \begin{aligned}  \phi_l(y) &= a_l \sin \left(\frac{ly}{R}\right) + b_l \cos \left(\frac{ly}{R} \right) \\   \end{aligned}}

Eq. (2.121):

\displaystyle{  \begin{aligned}  \phi_l(y) &= \phi_l(y+2\pi R) \\   \end{aligned}}

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\displaystyle{  \begin{aligned}  Z &= \sum_{k} \sum_{l} e^{- \beta E_{k,l}} \\    &= \sum_{k} \sum_{l} \exp\left\{- \beta \left( \frac{\hbar^2}{2m} \right) \left[ \left(\frac{k \pi}{a} \right)^2 + \left(\frac{l}{R}\right)^2 \right]\right\} \\  &= Z(a) \tilde{Z}(R) \\     \end{aligned}}

\displaystyle{  \begin{aligned}  Z(a) &= \sum_{k=1}^\infty \exp\left[- \beta \left( \frac{\hbar^2}{2m} \right) \left(\frac{k \pi}{a} \right)^2 \right] \\  \tilde Z (R) &= \sum_{l=-\infty}^\infty \exp\left[- \beta \left( \frac{\hbar^2}{2m} \right) \left(\frac{l}{R}\right)^2 \right] \\  &= \sum_{l=-\infty}^{-1} \left( \dotsb \right) + \sum_{l=0} \left( \dotsb \right) + \sum_{l=1}^\infty \left( \dotsb \right) \\  &= 1 + 2 Z(R \pi) \\  \end{aligned}}

— Me@2022-01-19 08:45:05 PM

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2022.01.26 Wednesday (c) All rights reserved by ACHK